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Simplifying 3n2 + -2n + -8 = 7n2 + 5n Reorder the terms: -8 + -2n + 3n2 = 7n2 + 5n Reorder the terms: -8 + -2n + 3n2 = 5n + 7n2 Solving -8 + -2n + 3n2 = 5n + 7n2 Solving for variable 'n'. Reorder the terms: -8 + -2n + -5n + 3n2 + -7n2 = 5n + 7n2 + -5n + -7n2 Combine like terms: -2n + -5n = -7n -8 + -7n + 3n2 + -7n2 = 5n + 7n2 + -5n + -7n2 Combine like terms: 3n2 + -7n2 = -4n2 -8 + -7n + -4n2 = 5n + 7n2 + -5n + -7n2 Reorder the terms: -8 + -7n + -4n2 = 5n + -5n + 7n2 + -7n2 Combine like terms: 5n + -5n = 0 -8 + -7n + -4n2 = 0 + 7n2 + -7n2 -8 + -7n + -4n2 = 7n2 + -7n2 Combine like terms: 7n2 + -7n2 = 0 -8 + -7n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 7n + 4n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 7n + 4n2)' equal to zero and attempt to solve: Simplifying 8 + 7n + 4n2 = 0 Solving 8 + 7n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + 1.75n + n2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.75n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + 1.75n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.75n + n2 = 0 + -2 1.75n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.75n + n2 = -2 The n term is 1.75n. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75n + 0.765625 + n2 = -2 + 0.765625 Reorder the terms: 0.765625 + 1.75n + n2 = -2 + 0.765625 Combine like terms: -2 + 0.765625 = -1.234375 0.765625 + 1.75n + n2 = -1.234375 Factor a perfect square on the left side: (n + 0.875)(n + 0.875) = -1.234375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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